Partial coordination number and contact proportion of densely packed binary random mixtures of quasi-two-dimensional granular materials

The partial coordination number and contact proportion associated with different contact types are key microscale parameters for understanding the macroscopic behavior of granular mixtures. However, experimental data for binary mixtures with large size ratios remain scarce, and direct comparisons among the Dodds, Clusel, and Biazzo models are lacking, hindering a comprehensive evaluation of their predictive accuracy. Moreover, the hypothesis proposed by Biazzo et al. (2009) that significant prediction discrepancies at large size ratios arise from the presence of numerous rattlers has not yet been experimentally supported. To address these gaps, we conducted a series of high-resolution optical experiments on two-dimensional (2D) dense binary mixtures with size ratios α=3, 5, 7, and 9. Our findings confirm the validity of Dodds and Biazzo models for lower size ratios (1<α<6.46). For large size ratios (α>6.46), the positive correlation between fine rattler fraction and prediction errors not only probably supports Biazzo et al.’s hypothesis but also suggests that excluding fine rattlers from the theoretical input may improve model accuracy. Quantitatively, the Dodds and Biazzo models outperform the Clusel model, with Biazzo's model showing slightly better predictive accuracy due to its incorporation of spatial correlations. However, the Dodds model offers practical simplicity owing to its lower parameter requirements. This study provides a practical basis for accurately characterizing local packing structures and their relation to macroscopic properties in 2D granular systems, but also lays a foundation for modeling more complex 3D systems.